Theorem 6.1 ([1]}) 
Let \( \alpha \in \mathrm {DC}_d(\gamma ,\tau ) \) , \( v\in C^k(d,{\mathbb {R}}) \)  with \( k\ge 550\tau \) . Then there exists \( \epsilon _*=\epsilon _*(\gamma ,\tau ,d,k) \)  such that if \( |v|<\epsilon _* \) , then the integrated density of states \( N_{v,\alpha } \)  is \( \frac{1}{2}\) -Hölder continuous:
\(|N_{v,\alpha }(E+\epsilon )-N_{v,\alpha }(E-\epsilon )|\le C_0 \epsilon ^{\frac{1}{2}}, \ \forall \epsilon >0,\ \forall E\in {\mathbb {R}},\) 
